Available online at www.sciencedirect.com

Polar Science 2 (2008) 149e161http://ees.elsevier.com/polar/

Role of Antarctic ice mass balance in present-daysea-level change

C.K. Shum a,*, Chung-yen Kuo b, Jun-yi Guo a

a Geodetic Science, School of Earth Sciences, The Ohio State University, 125 S Oval Mall, 221B Mendenhall Lab,

Columbus, OH 43210-1398, USAb Department of Geomatics, National Cheng-Kung University, Taiwan, ROC

Received 3 April 2007; revised 11 April 2008; accepted 23 May 2008

Available online 12 June 2008

Abstract

The Antarctic ice sheet is arguably the most critical in terms of future sea-level rise, primarily because it contains w70% of theworld’s fresh water. While there exists evidence of accelerated ice-sheet ablation during the past decade, the possibility that the icesheets contributed little to 20th century sea-level rise could result in Antarctica becoming the largest contributor to sea-level riseduring the 21st century. Here we review the findings of studies published following the 2007 Intergovernmental Panel for ClimateChange (IPCC) study, focusing on the role of Antarctica in present-day (1992e2006) sea-level rise. We show that the choice ofglacial isostatic adjustment (GIA) model significantly affects GRACE-estimated Antarctic mass loss, adding 0.25e0.45 mm/yrto the estimate of sea-level rise. The current estimate of Antarctica’s contribution to sea-level rise has a wide range: from�0.12 toþ0.52 mm/yr. The discrepancy between observed sea-level trend of 1.8 mm/yr and those estimated from various geophys-ical sources (2.10� 0.99 mm/yr) is 0.30 mm/yr. The role of Antarctica in sea-level rise might be better constrained by lengtheningsatellite observations, using long-term GPS data to discriminate subglacial vertical motion from ice mass balance, and detecting thesea-level signal due to elastic loading from the melting ice-sheets.� 2008 Elsevier B.V. and NIPR. All rights reserved.

Keywords: Antarctic ice sheet mass balance; Sea level; Satellite geodesy; Glacial isostatic adjustment; International Polar Year

1. Linkages among climate change,ice sheets, and sea level

The Earth’s Quaternary climate, driven by Milanko-vitch cycles that produced a succession of ice ages, canbe characterized at time-scales of 100,000 yrs (Zachoset al., 2001), with interlinked changes in temperature,

* Corresponding author. Tel.: þ1 614 292 7118; fax: þ1 614 292

7688.

E-mail address: ckshum@osu.edu (C.K. Shum).

1873-9652/$ - see front matter � 2008 Elsevier B.V. and NIPR. All rights

doi:10.1016/j.polar.2008.05.004

greenhouse gases (dominated by CO2), and global wa-ter reservoirs (including the cryosphere, hydrosphere,and sea level) over the past 3 million years. Since themost recent of these cycles, the Last Glacial Maximum(LGM; 19,000e30,000 yrs before present),50� 106 km3 of land ice has melted, leading to a risein global sea level of w130 m (Lambeck et al.,2002). During the 20th century, anthropogenic effectsthat led to global warming resulted in accelerated icemelt and a rapid rise in global sea-level (Bindoffet al., 2007). Paleoclimatic evidence obtained from

reserved.

150 C.K. Shum et al. / Polar Science 2 (2008) 149e161

past ice sheets (130,000e127,000 yrs before present)indicates that the rate of future ice-sheet melting andthe corresponding rate of sea-level rise due to climatechange could be higher than previously thought(Overpeck et al., 2006).

The 2007 Intergovernmental Panel for ClimateChange (IPCC) Fourth Assessment Report (FAR;Working Group I, The Physical Science Basis)concluded that warming of the climate system isunequivocal, and expressed a very high level of confi-dence in the proposal that the effects of human activi-ties since 1750 have resulted in global warming.Observational evidence confirms increasing trends inglobal average air, land, and ocean temperatures, themelting of snow and ice, and sea level.

Ice sheets are one of the dominant sources contrib-uting to present-day (w1990 to present) sea-level rise,and will most likely make a dominant contribution tofuture sea-level rise. Indeed, there exists evidence ofaccelerated thinning of the margins of the Greenlandand West Antarctic ice sheets over the past decade,attributable to anthropogenic warming (Alley et al.,2005; Lemke et al., 2007; Shepherd and Wingham,2007; Vaughan, 2005). The current Antarctic ice sheetcontains w90% of the world’s ice (or w70% of theworld’s fresh water). Some 98% of Antarctica is cov-ered by ice sheets of at least w1.6 km thick; completemelting of this ice would raise the global sea-level by56.6 m. The present-day Antarctic ice sheet covers anarea of w12.3� 106 km2, with an ice volume of24.7� 106 km3 (Lythe et al., 2001), representingapproximately half of its size at the LGM(w21,000 yrs ago; e.g., Bentley, 2004).

The West Antarctic ice sheet is bedded well belowsea level, with its edges flowing into floating iceshelves; this sheet is considered unstable. In contrast,the East Antarctic ice sheet is relatively stable, andits bed is situated well above sea level. The Greenlandice sheet has a present-day average ice thickness ofw1.6 km and volume of 2.9� 106 km3, covering anarea of w1.7� 106 km2. Complete melting of theGreenland ice sheet would raise the global sea levelby 7.3 m (Bamber et al., 2001). Estimates of imbalancein the Greenland ice sheet, based primarily on geologicfield data and numerical modeling, vary from e130 toþ130 Gigaton/yr (resulting in �0.36 mm/yr of globalsea-level change; e.g., Reeh, 1991), compared withan estimate of e500 to þ500 Gigaton/yr (�1.4 mm/yr) for the Antarctic ice sheet (e.g., Bentley, 2004). Itis likely that the Antarctic ice sheet is still reactingdynamically to the glacialeinterglacial transition thatoccurred between 20,000 and 10,000 yrs ago, resulting

in an increase in the rate of snow accumulation duringthe last century (Bentley, 2004). About half of the icelost from Greenland is lost via surface melting;however, surface melting is much less important tothe mass balance of Antarctica (Lemke et al., 2007).

Despite the fact that the polar regions play a keyrole in global climate change, they remain poorlyobserved compared with other regions of the world.The Antarctic ice sheet, given its vast size and remotelocation, is the most poorly observed region in theworld. The First International Polar Year (IPY), heldin 1882e1883, was proposed by Georg Neumayerand inspired by an Austro-Hungarian naval officer,Karl Weyprecht (see http://www.ipy.org). The secondIPY (1932e1933) involved 44 participating nations,and led to an initial proposal for polar observationprograms. The current IPY (2007e2008), sponsoredby the International Council for Science and the WorldMeteorological Organization (WMO), has more than30 participating nations (see http://www.ipy.org). Sincethe last IPY 75 yrs ago, significant advances in obser-vational technologies (in particular space and in situgeodetic and remote sensing sensors, which are mostlyestablished as part of extensive international collabora-tions) have yielded continuous geophysical time seriesthat can be used to study the role of ice sheets in globalsea-level rise resulting from anthropogenic climatechange.

Antarctica is arguably the most critical region interms of future sea-level rise, primarily because of itscurrent retention of most of the world’s ice and freshwater. It is plausible that the ice sheets contributed lit-tle to sea-level rise during the 20th century (Cazenave,2006; Wingham et al., 2006); however, there exists ev-idence of accelerated ice-sheet ablation or melt duringthe past decade (w1992e2006; Lemke et al., 2007;Shepherd and Wingham, 2007). This trend could po-tentially result in the scenario that Antarctica becomesthe largest contributor to sea-level rise during the 21stcentury, surpassing the contribution of Greenland.

This paper summarizes the findings of studiespublished since the 2007 IPCC FAR Sea Level Assess-ment, focusing on the role of Antarctic ice sheet massbalance on present-day (1992e2006) sea-level rise,primarily based on satellite geodetic observationsfrom satellite radar altimetry and gravimetry (GravityRecovery and Climate Experiment, or GRACE).

2. Sea level rise over the past 500 yrs

More than 70% of Earth is covered by oceans, and itis anticipated that most of the population in the world

151C.K. Shum et al. / Polar Science 2 (2008) 149e161

will be living within 100 km of the coast by 2020. Sea-level rise is widely recognized as one of the conse-quences of anthropogenic climate change, and hasa substantial social and economic impact. Quantifying,understanding, and predicting sea-level change remaina complex interdisciplinary problem. The low rate ofsea-level rise recorded during the last century(1e2 mm/yr) can only be partially explained bycomplex, interacting geophysical processes within theEarth system, including interactions among thesolid Earth, atmosphere, ocean, cryosphere, andhydrosphere.

To highlight the problem of global climate change,including sea-level rise, the WMO and the United Na-tions Environment Programme established the IPCC in1988. The IPCC First Assessment Report estimatedglobal sea-level rise during the 20th century to havebeen 1.0e2.0 mm/yr, although with a high degree ofuncertainty (Warrick and Oerlemans, 1990). TheIPCC Second Assessment Report found greater con-sensus on an estimate of w2 mm/yr for sea-level riseduring the 20th century, attributing half of this rise tothermal expansion of the ocean and glacier melting(Warrick et al., 1996). The IPCC Third AssessmentReport (TAR) provides a ‘‘central’’ estimate of globalsea-level rise during the 20th century of 1.5 mm/yr(Church et al., 2001), with greater certainty towardan observed value of 1.84� 0.35 mm/yr (Douglas,2001), as derived from 27 long-term (>70 yrs) tide-gauge records.

A significant result at this time was the observedthermal expansion of the ocean over the past 40 yrs,which is estimated to be 0.55 mm/yr (Levitus et al.,2000). This estimate is almost half of the value of1 mm/yr speculated by the 1996 IPCC Assessment,thus significantly broadening the gap between observedsea-level rise (1.84 mm/yr) and geophysical explana-tions. Specifically, geophysical causes are believed tototal just 1.1 mm/yr of sea-level rise over the pastcentury (0.6 mm/yr from melt water and 0.5 mm/yrfrom steric effect; Church et al., 2001). This discrep-ancy (40% difference) between observed and explainedsea-level rise led Munk (2002) to proclaim a ‘‘sea-levelenigma.’’ To account for the 1.2 mm/yr of ‘‘residual’’sea-level rise, if explained solely in terms of meltwater, would require w400 Gigaton/yr of fresh water,or, if explained solely in terms of the thermostericeffect, would require w10� 1021 J/yr of excess heatstorage in the ocean; neither of these scenarios isconsidered at all likely. Since 2001, this discrepancyhas been significantly narrowed as the result of numer-ous studies that have sought to improve the accuracy of

sea-level observations, modeling, and geophysicalinterpretations (e.g., Cazenave and Nerem, 2004;Chao et al., 2002; Church et al., 2004; Church andWhite, 2006; Meier and Wahr, 2002; Mitrovica et al.,2001).

Compared with IPCC TAR, the 2007 IPCC FourthAssessment Report Sea Level Assessment (Bindoffet al., 2007; Lemke et al., 2007) significantly closedthe gap between observations and geophysical explana-tions. A review of observed sea-level rise (based ondata from tide gauges and satellite altimetry) andexplained geophysical sources (thermal expansion,ablation/accumulation of glaciers, ice caps, Greenlandand Antarctica ice sheets) yields figures of 1.8� 0.5and 1.1� 0.5 mm/yr during 1962e2003, and3.1� 0.7 and 2.8� 0.7 mm/yr during 1992e2003,respectively (Bindoff et al., 2007; Lemke et al.,2007). Sea-level observations during 1992e2003were based on TOPEX/POSEIDON radar altimetry(Cazenave and Nerem, 2004; Church et al., 2004),representing global measurements (in contrast to thelocal nature of tide-gauge records). Estimates of thecontribution of the Antarctic ice sheet to sea-levelrise are 0.14� 0.41 mm/yr during 1961e2003 and0.21� 0.35 mm/yr during 1993e2003, indicatinga higher melt rate over the past decade. However, theagreement obtained between observations andgeophysical explanations could be merely a coinci-dence, as large uncertainties remain (Cazenave,2006), including uncertainties in estimates of ice-sheetmass balance and knowledge of other geophysicalsources, including hydrologic imbalance due to thenatural (Milly et al., 2003) and human impoundmentof water (Sahagian et al., 1994).

Fig. 1 shows the estimated, observed, and predictedsea-level rise for a period of 600 yrs (1500e2100),demonstrating the so-called ‘‘hockey stick’’ trend ofsea-level rise, characterized by a significant accelera-tion in sea-level rise since 1900 coinciding with theIndustrial Revolution. Pre-1900 estimates are basedon geological interpretations (0.1e0.2 mm/yr; Peltier,2004; Lambeck et al., 2002), and observed sea-levelrise (1900e2005) is based on tide-gauge data andTOPEX satellite altimetry (Cazenave and Nerem,2004; Church et al., 2004; Miller and Douglas,2006). The observed sea-level rise shown in Fig. 1 isbased on data from tide gauges and from multiple mis-sion satellite altimetry (1985e2005), includingTOPEX data (Kuo, 2006).

In compiling a time series of globally averaged sea-level data (red curve for tide-gauge data in Fig. 1 andblue curve for satellite altimetry data), Kuo (2006)

Fig. 1. Estimated, observed, and predicted global sea-level rise over the period 1500e2100.

152 C.K. Shum et al. / Polar Science 2 (2008) 149e161

used 585 tide-gauge records, spanning 1990e2002,and multiple satellite radar altimetry data from GeosatGM/ERM, ERS-1, ERS-2, TOPEX, GFO, ENVISAT,and JASON-1 over the period 1985e2002 (witha data gap between 1988 and 1991). The sea-levelrise estimated from the long-term tide-gauge time-series is 1.6� 0.2 mm/yr, and that from satellite altim-etry is 3.0� 0.4 mm/yr. With a much shorter data span(w15 yrs as compared to over 50 yrs for tide-gaugerecords), the altimetry estimate is potentially influ-enced by interannual or longer oceanic variations.

The hindcast and predicted sea level is based on‘‘natural’’ forcing (NAT500) and ‘‘natural’’ plus green-house gases (ALL250) using the HadCM3 climatemodel (courtesy of J. Gregory, University of Reading,UK; Gregory et al., 2006), indicating that the worst-case scenario (ALL250; pink envelope (2005e2100)in Fig. 1) could lead to a 60 cm rise in global sea-levelby 2100. Recent studies have predicted significantlyhigher sea-level rise during the 21st century (e.g.,0.5e1.4 m above the 1990 level, as predicted byRahmstorf, 2007) than that predicted by IPCC FAR(0.4e0.6 m; Fig. 1); such predictions remain a topicof controversy.

2.1. Recent estimates of geophysical contributionsto 20th century sea-level rise

The ice sheets are one of main contributors to sea-level rise, especially given the accelerated rate ofpresent-day (1990 to present) melting due to anthro-pogenic climate forcing. Other geophysical factorsinclude the melting of mountain glaciers (Dyurgerovand Meier, 2005), thermal expansion of the ocean(Ishii et al., 2006; Levitus et al., 2005), potential

hydrologic imbalance (Milly et al., 2003; Ngo-Ducet al., 2005), and the extraction of ground water andstorage of water in artificial reservoirs (Sahagianet al., 1994). The magnitudes of the last two of thesegeophysical sources remain largely unknown orcontain large uncertainties (Bindoff et al., 2007).Satellites and airborne sensors have provided mostof the continent-wide observation data recordedduring the past 15 yrs.

Here we summarize the results of recent studies,some not covered by the 2007 IPCC FAR, includingan examination of those factors that affect estimatesof Antarctic ice-sheet mass balance (e.g., warm-watercalving of ice shelves, dynamic response of ice sheetsto warming, buttressing, and the potential impact ofsubglacial lake dynamics). Table 1 lists the respectivecontributions of estimated sea-level trends (rate ofrise in equivalent sea-level) from various plausiblegeophysical sources.

It is evident from Table 1 that the estimated present-day contributions of the Greenland and Antarctic icesheets to global sea-level rise are highly uncertain,with uncertainties larger than the estimates. Estimatesof Greenland’s contribution to sea-level rise varyfrom �0.03 to 0.57 mm/yr, based on InterferometricSynthetic Aperture Radar (InSAR), airborne laser al-timetry, and decadal radar altimetry (Geosast, ERS-1,ERS-2) (Abdalati et al., 2001; Johannessen et al.,2005; Krabill et al., 2004; Rignot and Kanagaratnam,2006; Rignot and Thomas, 2002; Zwally et al.,2005); estimates based on GRACE data range from0.3 to 0.63 mm/yr (w2003 to 2006) (Chen et al.,2006a; Luthcke et al., 2006; Ramillien et al., 2006;Velicogna and Wahr, 2006a). Estimates of the sea-levelchange attributed to melting of the Antarctic ice sheet

Table 1

Current estimates of sea-level trends from geophysical sources

Geophysical sources Sea-level contributions (mm/yr)

Thermosteric

(1950e2003)

0.4

(Levitus et al., 2005; Ishii et al., 2006)

Glaciers and ice caps

(1961e2004)

0.51 to 0.8

(Arendt et al., 2002; Dyurgerov and Meier,

2005; Kaser et al., 2006). Summary:

0.66� 0.15 mm/yr

Greenland ice sheet

(1992e2005)

�0.03 to 0.57

(Abdalati et al., 2001; Rignot and Thomas,

2002; Krabill et al., 2004; Zwally et al., 2005;

Johannessen et al., 2005; Rignot &

Kanagaratnam, 2006); 0.3 to 0.63

(Ramillien et al., 2006; Luthcke et al., 2006;

Chen et al., 2006a). Summary:

0.30� 0.33 mm/yr

Antarctic ice sheet

(1992e2006)

�0.12 to 0.17

(Thomas et al., 2004; Davis et al., 2005;

Wingham et al., 2006; Zwally et al., 2005);

0.14 to 0.52

(Ramillien et al., 2006; Chen et al., 2006b;

Velicogna and Wahr, 2006a,b; this study).

Summary: 0.20� 0.32 mm/yr

Hydrologic 0.0 to 0.12

(Milly et al., 2003; Ngo-Duc et al., 2005).

Summary: 0.06� 0.06 mm/yr

Anthropogenic 0.05 (Sahagian et al., 1994)

Total 1.11 to 3.01 mm/yr, or 2.10� 0.99 mm/yr

153C.K. Shum et al. / Polar Science 2 (2008) 149e161

range from �0.12 to 0.17 mm/yr (Davis et al., 2005;Thomas et al., 2004; Wingham et al., 2006; Zwallyet al., 2005), based on InSAR and decadal satelliteradar altimetry (Geosat, ERS-1, and ERS-2); estimatesbased on GRACE data range from 0.14 to 0.52 mm/yr(Chen et al., 2006b; Ramillien et al., 2006; Velicognaand Wahr, 2006b). It should be noted that the GRACEdata reported in the literature spans a period of only3 yrs (2002e2005), and thus these estimates could becontaminated by interannual or longer periodicvariations.

In summary, after taking into account thermalexpansion of the ocean (Ishii et al., 2006; Levituset al., 2005), recent accelerated melting of glaciersand ice caps (Arendt et al., 2002; Dyurgerov andMeier, 2005; Kaser et al., 2006), and other effects,the total contribution of plausible geophysical sourcesto global sea-level rise ranges from 1.11 to 3.09(2.10� 0.99) mm/yr (Table 1). Compared with recentobserved sea-level rise during the 20th century(1.6� 0.2 mm/yr by Kuo, 2006; 1.84� 0.35 mm/yrby Church et al., 2004 and Douglas, 2001), thegeophysical budget (Table 1) is in better agreementwith the observed sea-level trend, with a discrepancyof w0.4 mm/yr (Table 1, comparing the respective

lower and upper estimates), than the 2001 IPCC TARSea Level Assessment (Church et al., 2001). However,this agreement could be coincidental because largeuncertainties remain in the estimates of individualcontributors to sea-level rise, in particular the contribu-tions from the Greenland and Antarctic ice sheets.

There is also a discrepancy between observed ice-sheet melt/thickening and corresponding changes inlocal and global sea level, possibly reflecting the factthat the satellite measurements used to determine thecontribution of ice melting to global sea level span a pe-riod of just 15 yrs. Here we chose to compare the long-term sea-level trend derived from tide-gauge data (asthe preferred observed sea-level trend) with sea-levelchange arising from geophysical sources, rather thanusing altimetry-based estimates with global coveragebut with a much shorter time series. This decisionwas made because of the possibility that the altime-try-derived trend could be dominated by interannualor longer oceanic variations.

The results of this study, which post-date the 2007IPCC TAR Sea Level Assessment, yield a value of2.10� 0.99 mm/yr from various geophysical sources,much closer to the observed sea-level trend of1.8 mm/yr than the IPCC FAR assessment of1.1� 0.5 mm/yr (1961e2003); however, as statedabove, this agreement could be entirely coincidental,as large uncertainties exist in the estimates of ice-sheetmass balance and other contributing factors.

3. Discrepancies in estimates of Antarcticice-sheet mass balance

In addition to the potential measurement errors thatadd to the large discrepancies in the contribution ofmelting of the Antarctic ice sheet to global sea level(Table 1), plausible geophysical explanations include(1) the intrusion of warm water deep beneath theAntarctic floating ice shelves, which is speculated tolead to collapse of the ice shelves or the formation ofpolynas (Jacobs et al., 1992; Shepherd et al., 2004);(2) potential ice-sheet instability due to the dynamicsof large subglacial lakes resulting from faster-flowingice streams due to accelerated melting (Bell et al.,2007; Fricker et al., 2007; Wingham et al., 2006); (3)ice-shelf buttressing/sedimentation that acts to stabilizeice-sheet grounding lines (Alley et al., 2007; Anandak-rishnan et al., 2007; Dupont and Alley, 2005); (4) gla-cial dynamics leading to ice-sheet instability (Shepherdand Wingham, 2007); and (5) geodynamic processesarising from interaction between ice and solid Earthdue to GIA (Ivins and James, 2005) and due to

154 C.K. Shum et al. / Polar Science 2 (2008) 149e161

present-day ice melting (elastic deformation), resultingin the deformation of the subglacial topography.

Alley et al. (2007) suggested that sedimentationbeneath ice shelves helps to stabilize ice sheets againstretreat, implying that recent changes in the Antarcticice sheet may not have fully contributed to sea-levelrise, even though climate warming has driven Antarcticmass loss. Furthermore, controversy exists regardingthe contribution of the East Antarctic ice sheet tosea-level change. Davis et al. (2005) reported a thicken-ing of the East Antarctic ice sheet based on decadalsatellite radar altimetry observations (1992e2003),while Monaghan et al. (2006) documented an insignif-icant change in snowfall since the 1950s. Our currentinability to realistically model the dynamic responseof ice sheets to climate change (Alley et al., 2005)also contributes to our inability to fully explain causesof ice-sheet mass balance change, especially for theAntarctic ice sheet in which surface melting is ofrelatively minor importance.

Here we discuss and hypothesize upon plausiblescientific rationale (some of which have been discussedabove), and identify proposed observational methodol-ogies that might improve our quantification of Antarc-tic ice sheet mass balance, primarily using modernspace geodetic measurements.

3.1. Potential discrimination between glacialisostatic adjustment and ice mass balance

GIA and present-day ice loading are among themost prominent signals among satellite-measured

Fig. 2. Left: mass variations caused by present-day Antarctic ice melt and e

thickness change (cm/yr). Middle: effect of viscous mantle rebound, or gla

et al., 2002; Ivins and James, 2005; data courtesy of Erik Ivins, California In

left and middle figures represents the signal presumably observed by GRAC

erally variable 3D GIA models (Wang and Wu, 2006) (data courtesy of Pa

ice-sheet mass balance (i.e., GRACE), and to a lesserextent satellite altimetry, including radar altimetry(Wingham et al., 1998) and laser altimetry (ICESat;Schutz et al., 2005). Because GIA remains to be oneof the strongest signals in GRACE, it is difficult toseparate GIA and ice mass balance over ice sheets(Wahr et al., 2000), as opposed to over regions offormer ice sheets such as Laurentia and Fennoscandia.

Fig. 2 (left) shows mass variations caused bypresent-day Antarctic ice melt and elastic loading dueto present-day ice melt (based on a variety of modernobservations, including InSAR) in terms of equivalentwater thickness change (left), the effect of viscousmantle rebound (or glacial isostatic adjustment, GIA)in Antarctica (middle) computed using the ‘‘Ivins &James model’’ (Ivins et al., 2002; Ivins and James,2005; data courtesy of Erik Ivins, California Instituteof Technology/Jet Propulsion Laboratory, USA), andthe total effect of elastic loading resulting from pres-ent-day ice melt and GIA (left and middle figures com-bined, not shown here), which is the signal presumablyobserved by GRACE in addition to the ice mass bal-ance and other signals. Note that the elastic loadingfrom present-day ice melt and GIA results in subglacialtopographic uplift, which must be known to accuratelyestimate ice-sheet mass balance. Fig. 2 (right) showsthe effect of a laterally varying (in terms of viscosityand mantle thicknesses) 3D GIA model (Wang andWu, 2006; Wu, 2004) (data courtesy of Patrick Wu,University of Calgary, Canada; hereafter referred toas the ‘‘Wu model’’). Fig. 2 (middle and right) showsthe substantial difference between the Ivins & James

lastic loading due to present-day ice melt, in terms of equivalent water

cial isostatic adjustment (GIA) using the Ivins & James model (Ivins

stitute of Technology/Jet Propulsion Laboratory, USA); the sum of the

E in addition to mass balance and other signals. Right: effect of lat-

trick Wu, University of Calgary, Canada).

155C.K. Shum et al. / Polar Science 2 (2008) 149e161

and Wu models, with the Wu model showing muchlarger GIA signals. Significant differences have alsobeen observed between these models and the ICE-5Gmodel using the ICE-5G deglaciation history (Peltier,2004) and the 3D Wu model. The significant degreeof uncertainty in the GIA models highlights the diffi-culties involved in the current approach adopted to re-move the GIA effect using a forward model to estimatethe Antarctic ice-sheet mass balance.

Fig. 3 provides an updated analysis of GRACE-estimated Antarctic ice mass balance, including a lon-ger time series (April 2002eNovember 2006) than thatused by Velicogna and Wahr (2006b) (April 2002eAugust 2005). The GRACE-computed water thickness,Dh (cm), can be calculated according to Wahr et al.(1998) as follows:

Dhðq;lÞ ¼ asE

3sw

XN

n¼0

Xn

m¼0

Pnmðcos qÞð2nþ 1Þðknþ 1Þ

� ðDCnm cosðmlÞ þDSnm sinðmlÞÞ

where DCnm and DSnm are the geopotential sphericalharmonic coefficient change (here we use the differencebetween the monthly GRACE geopotential solution anda reference model, the GGM01S from the University ofTexas Center for Space Research), a is the radius ofEarth, n is degree and m is order, q is co-latitude and

Fig. 3. GRACE-estimated averaged Antarctic ice mass balance in

terms of water thickness (April 2002eNovember 2006). The red

curve indicates the ice thickness corrected for an annual component

of geocenter correction and hydrologic signal leakage (data courtesy

of John Wahr, University of Colorado, USA) using the GDLAS hy-

drologic model. The blue curve is the water thickness after correcting

for GIA, using the ICE-5G model. (For interpretation of the refer-

ences to colour in this figure legend, the reader is referred to the

web version of this article.)

l is longitude, kn is the load Love number of degree nthat describes the Earth’s elastic deformation, Pnm isthe fully normalized associated Legendre function, sw

is the density of water (1000 kg/m3), and sE is theaverage density of the Earth (5517 kg/m3). Antarcticice-sheet mass balance is computed using the above for-mula for each of the monthly GRACE gravity solutions,followed by simultaneously estimating a trend (changein Dh) and the annual and semi-annual signals using theGRACE time series over Antarctica. A change in waterthickness of 1 cm/yr over the region of grounded ice inAntarctica is equivalent to approximately 0.33 mm/yrof equivalent change in global sea level.

We used the University of Texas Center for Space Re-search (CSR) GRACE data product Release 4 (http://www.csr.utexas.edu/grace; April 2002eNovember2006, red curve in Fig. 3, in the form of water thicknessexpressed in centimeter), corrected for an annual com-ponent of geocenter correction and hydrologic leakageusing a global hydrologic model, GDLAS (data courtesyof John Wahr, University of Colorado, USA). The bluecurve in Fig. 3 is the GRACE-observed ice thickness(water thickness) time series after removing GIA usingthe ICE-5G (VM2) model. The temporal resolution ofboth time series (red and blue curves) is monthly, andthe lighter (red and blue) vertical bars indicate estimateduncertainty (w3 cm) for each monthly data point. Thetrend of the red curve is �0.06� 0.24 cm/yr (theGRACE trend is �0.18� 0.24 cm/yr, and the hydro-logic leakage trend is �0.13� 0.02 cm/yr). Thepredicted GIA varies with the choice of model:0.75 cm/yr from the Ivins & James model, 1.03 cm/yrfrom the ICE-5G (VM2) model, and 1.37 cm/yr fromthe Wu model. As a result, the estimated Antarctic ice-sheet mass balance is �0.81� 0.24 cm/yr (Ivins &James model),�1.09� 0.24 cm/yr (ICE-5G, blue curvein Fig. 3), or �1.43� 0.24 cm/yr (Wu model), corre-sponding to an equivalent sea-level rise of 0.27� 0.08,0.36� 0.08, or 0.48� 0.08 mm/yr, respectively.

It is clear that mismodeling of GIA could signifi-cantly influence the GRACE-derived ice mass balanceestimate of the Antarctic ice sheet by almost a factor of2, with the Wu model providing the largest apparentAntarctic mass imbalance estimates. Another errorsource is the secular trend of the so-called geocentercorrection, which is not included in the GRACEtemporal gravity model solutions and could affectestimates of ice-sheet mass balance (Chambers et al.,2007). Because GRACE is a two-satellite system, thedifferential measurement (satellite-to-satellite ranging)diminishes GRACE’s sensitivity to the so-calledgeocenter motion, which is the modeling of the

Fig. 4. Antarctic ice mass balance in terms of ice thickness, as deter-

mined by ERS-1/-2 radar altimetry (1991e2002).

156 C.K. Shum et al. / Polar Science 2 (2008) 149e161

degree-one terms (C10, C11, S11) that represent thelongest wavelength components of the Earth’s geopo-tential. Previous simulations and other analyses haveshown that neglecting the secular component of thegeocenter model or correction could be significantfor ice sheet mass balance estimates using GRACE(Chambers et al., 2007). At present, the geocentercorrection determined using satellite laser ranging(SLR) is reasonably robust in the seasonal componentbut unreliable in the secular component (Tapley et al.,2004).

The proposed rationale and approach to discriminat-ing GIA from ice-sheet mass balance are based on theavailability of measurements of surface height change(GPS and/or satellite/airborne altimetry) and gravitymeasurements (absolute gravimetry and/or GRACE)(Velicogna and Wahr, 2002; Wahr et al., 1995, 2000).Wahr et al. (2000) and Velicogna and Wahr (2002)discussed an approach that employed ICESat-measured changes in ice sheet thickness andGRACE-observed changes in ice mass to separateice-sheet mass balance and GIA over Antarctica usingsimulation studies. ICESat measurements over the icesheets (e.g., Harpold et al., 2006) currently covera relatively short time period (2003e2006), and areunable to deliver a continuous observed time seriesof 5 yrs or longer due to problems associated withthe laser instrument. Therefore, the potential separationof GIA and ice-sheet mass changes must rely on datasets in addition to ICESat.

One potential approach to separating ice sheet massbalance and GIA is to use radar altimeter data (ERS-1,ERS-2, and ENVISAT, 1992e2006) with a much longertime span than ICESat. Fig. 4 shows the determinationof Antarctic ice-sheet mass balance during 1991e2002based on combined ERS-1 and ERS-2 radar altimetryusing a technique reported by Wingham et al. (1998)that processes ERS radar altimetry and converts theice elevation change to ice thickness change by correct-ing for firn compaction. It is envisioned that the use ofENVISAT elevation time series, concurrent withGRACE gravimetry time series, and ICESat elevationchanges based on crossover measurements will poten-tially lead to improved estimates of the Antarctic ice-sheet mass balance.

An independent solution to the problem of determin-ing vertical motions of subglacial bedrock (i.e., resultingfrom GIA and elastic deformation due to present-day icemelt) will arrive with the planned polar network(POLENET; http://www.tu-dresden.de/ipg/polenet) ofcontinuous GPS receivers to be established on bedrockthroughout the Antarctic continent, in addition to

existing GPS networks (Dietrich et al., 2004). GPS mea-surements will then yield 3D velocity data, providing anadditional constraint on the separation of geodynamics(including GIA, elastic deformation, and tectonics)and ice-sheet mass balance over Antarctica.

4. Loading effect from present-dayice melt and sea level

Classical sea-level theory has become well estab-lished in the literature (e.g., Farrell, 1972; Wahret al., 1998). Mitrovica et al. (2001), Tamisiea et al.(2001), and Plag (2006) extended sea-level theory toinclude anticipated elastic loading in computing sea-level trends based on present-day ice-melt sources(Antarctica, Greenland, and mountain glaciers). Theexchange of water among ice, land, and ocean isone of the driving forces of sea-level change;however, this exchange does not influence sea levelin a uniform way. If the period of the exchange issufficiently long, the ocean surface could be approxi-mately considered as an equipotential surface. Thistheoretical relationship could be used to computethe relative sea-level change due to the above-mentioned mass exchange over all oceans, providedthat variations in water storage over land are known.The elastic loading effect (i.e., solid-Earth deforma-tion due to the mass variation of the exchange) shouldalso be taken into account.

157C.K. Shum et al. / Polar Science 2 (2008) 149e161

Mitrovica et al. (2001) computed a normalizedgeographical pattern of the sea-level trend (mm/yr)due to a uniform present-day ice melt originatingfrom Antarctica as a single melt source. Because themelting rate of the ice source is assumed to be uniformand large to raise global sea level by 1 mm/yr, the re-sulting sea-level change involves reduced sea level inareas near Antarctica and increased sea level in thefar field. This result represented a pioneering work interms of linking ice-sheet mass balance, geodynamics,and sea level: if the signal is measurable in the ocean, itcould provide an additional constraint of ice-sheetmass balance using geodynamics (elastic loading the-ory). However, the assumption of uniform melt fromthe Antarctic ice sheet is unrealistic.

Wake et al. (2006) also discussed the problem thatarises from the fact that the thermosteric sea level islarge and with complex spatial variations, therebyaccounting for a major portion of the sea-level changesignal derived from tide-gauge records along the eastcoast of the USA, overwhelming the sea-level signalpotentially generated by the loading effect resultingfrom melting of the Greenland ice sheet. If tide-gaugeor bottom-gauge sites were available around or nearGreenland or Antarctica, producing steep sea-level-change gradients resulting from ice-sheet melt loading,these signals would potentially be separable from thethermal expansion of the ocean.

In this study, we used GRACE observations (CSRRelease 4 data product; Tapley et al., 2004) coveringthe period April 2002eNovember 2006 to computethe predicted elastic loading effect of sea-level trendsresulting only from mass changes (ice melt/accumula-tion) over Antarctica, not from other sources (see alsoFig. 3). We also corrected GRACE-observed Antarc-tic mass variations for the annual component of geo-center correction and hydrologic leakage (computedusing a GDLAS hydrologic model; e.g., Velicognaand Wahr, 2006b). The GIA effect, computed usingthe ICE-5G (VM2) model, was removed from theGRACE observations. We applied non-isotropicfiltering (Han et al., 2005b) (400� 800 km latitudeand longitude filtering radii, respectively) to theGRACE monthly solutions, and fitted semi-annual,annual, and secular (interannual) signals to the timeseries. The secular or interannual signal (Fig. 5,bottom left) shown here has not been statisticallyassessed to examine the robustness (e.g., divided bythe standard deviation). We then used an extendedand generalized loading theory (Guo and Shum,2005) to compute the sea-level change due to elasticloading of Antarctic ice melt using the GRACE

solutions in the annual and secular (interannual)components.

Fig. 5 (top left) shows the amplitude of annualmass variation from GRACE observations (April2002eNovember 2006) over Antarctica (millimeterof water thickness change). Fig. 5 (top right) showsthe corresponding amplitude of annual relative sea-level (geoid) change as a result of mass exchangebetween land and ocean around Antarctica (millime-ter of water thickness change). The figure in thebottom left shows the secular mass variation fromGRACE observations over Antarctica (mm/yr ofwater thickness change), and the figure in thebottom-right shows the secular sea-level trend as a re-sult of mass exchange between land and ocean aroundAntarctica (mm/yr of water thickness change). Theestimate of the secular signal has a large uncertaintyresulting from the limited time span (w4.5 yrs) ofGRACE observations.

Fig. 5 (bottom left) shows some of the anticipatedsignals over Antarctica: a large loss in ice mass(w3 cm/yr) in West Antarctica and a large mass gain(w2 cm/yr) in Enderby Land, presumably due tosnow accumulation or other causes. However, theorigin of the signal is presently unknown. A massgain is shown near the FilchnereRonne Ice Shelf(FRIS), probably due to errors in ocean tide (includingM2 and S2 errors; Han et al., 2005a). The mass loss inthe Ross Sea is over ice shelves, probably related to theuse of the ICE-5G GIA model. The bottom-right figureshows a sea-level pattern that differs substantially (andwith a slightly different magnitude) from the pattern ofsea-level change predicted when assuming uniformmelting of the Antarctic ice sheet (Mitrovica et al.,2001).

The sea-level signals, annual or secular, are up tothe level of 0.8 and 1 mm/yr, respectively, which couldpotentially be detected by ocean-bottom-pressuregauges or other sea-level measurements. If suchmeasurements were possible, additional observationalconstraints could be established via the relationship be-tween ice mass balance, geodynamics (elastic loading),and sea level, thereby improving providing a means toassess the ice mass balance estimates.

Despite these possibilities, there are very few oper-ational long-term tide gauges located near Antarctica(e.g., the Faraday (UK)eVernatsky (Ukraine) is thelongest tide recording site by the well-type tide gaugewhich is operational since 1960, and the JapaneseSyowa ocean-bottom-pressure instrument is thesecond longest site which is operational since 1976;Shibuya et al., 2005), compared with the 100þ year

Fig. 5. Top left: amplitude of annual mass variation from GRACE observations (April 2002eNovember 2006, Release 4 data product, see also

Fig. 3) over Antarctica (millimeter of water thickness). Top right: amplitude of annual relative sea-level change as a result of mass exchange

between land and ocean around Antarctica (millimeter of water). Bottom left: secular mass variation from GRACE observations over Antarctica

(mm/yr of water thickness change). Bottom-right: secular relative sea-level change as a result of mass exchange between land and ocean around

Antarctica (mm/yr of water thickness). The estimate of the secular change may suffer from the limited time span of GRACE observations (April

2002eNovember 2006).

158 C.K. Shum et al. / Polar Science 2 (2008) 149e161

records available from mid-latitude tide gauges. It isanticipated that testing of the hypothesis that ‘‘theelastic loading effect from present-day ice melt couldbe measured by sea-level instruments’’ will not be

possible until additional tide-gauge or bottom-gaugesites are installed around the Antarctic coastalmargins, especially at sites near the West Antarcticice sheet.

159C.K. Shum et al. / Polar Science 2 (2008) 149e161

5. Conclusions

Since the last International Polar Year 75 yrs ago,advances in observational technology have givenrise to a variety of polar-observing satellites that com-plement ongoing and extensive international collabo-rations in polar research. It is anticipated that thecurrent International Polar Year (2007e2008) willmake substantial progress in this regard, laying thefoundation for continuing in situ observations thatwill help to improve our quantification of the role ofthe Antarctic ice sheet in sea-level rise resultingfrom anthropogenic climate forcing. Current estimatesof Antarctic ice-sheet mass balance, as calculatedfrom a variety of satellite observations, have a widerange, from �0.12 to þ0.52 mm/yr. There existsevidence that the thinning of ice sheets has acceler-ated during the past decade, whereas the ice sheetswere generally in balance during the 20th century. Areview of recent studies, updating the 2007 IPCCSea Level Assessment, indicates that the currentsea-level budget is largely dominated by recent icesheet and glacier imbalances. The budget is moreclosely in agreement with the observed sea-level rise(of w1.8 mm/yr) than the 2001 IPCC TAR Sea LevelAssessment. It is found that the incomplete GIAsignal dominates the present-day mass balance signalobserved by GRACE. We show that GIA significantlyaffects GRACE-estimated Antarctic mass loss: it adds0.25e0.45 mm/yr to the estimate of sea-level rise,depending on the choice of GIA model. As proposedby Wahr et al. (2000), a combination of satellite altim-etry data and GRACE could potentially be used toseparate the GIA and ice mass balance signals. Theplanned POLNET GPS network, to be establishedon bedrock, could provide an independent data setof use in modeling GIA and other geodynamicsignals, as well as to improve estimates of Antarcticice-sheet mass balance. It is plausible that data fromtide gauges located around the melt source of theice sheet (i.e., near West Antarctica) could be usedto constrain the ice-sheet mass balance signal by pro-viding a relationship between the geodynamics (i.e.,elastic loading signals resulting from present-day icemelt) and local sea-level signal, thereby providingan independent verification of the Antarctic ice-sheetmass balance.

Acknowledgements

This research was supported by grants from NASA’sInterdisciplinary Science and GRACE Programs

(NNG04GN19G, NNG04GF01G), from NOAA/NEDIS (NA06NES4400007), and from NationalCheng-Kung University, Taiwan. The GRACE dataproducts are from UT/CSR and JPL. We thank theEditor-in-Chief and anonymous reviewers for theirconstructive comments that led to improvements inthe manuscript.

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